Solve Non-Linear Parabolic Partial Differential Equation by Spline Collocation Method

Abstract

This paper provides an overview of the formulation, analysis and implementation of Spline collocation method for the numerical solution of partial differential equation with two space variable which is of parabolic type. The method includes the solution of non-linear equation which can be expressed as in matrix form. The use of spline collocation methods in the solution of initial-boundary value problems for parabolic-type system id described, with emphasis on alternating direction implicit methods. Problem of vertical groundwater recharge solve by spline collocation method. Finally, recent applications of spline collocation method are outlined.